Answer: To encourage readers to envision freedom everywhere.
In this except, Martin Luther King Jr. is naming several locations in the United States in order to encourage readers to envision freedom everywhere. By naming places that are far apart, he highlights the fact that location will no longer be a problem for the exercise of freedom. Moreover, the second section of the except (after the phrase "but not only that") names places that are particularly contentious, and that continue to struggle with racial issues. His intention is to imply that even the most conflictive places will soon enjoy freedom for all.